New razor won't charge because of bad contact.

I have this brand new OneBlade that refuses to charge. Philips's customer service sent me a new one for free. But I'd like to fix the faulty one.

The charging cable attaches to the device firmly and everything looks fine, but the light on the razor doesn't turn on and it doesn't charge. I tried the new cable that Philips sent and still doesn't work. When I force-press and hold the cable into the device with a slight angle (pressing both into the device and down) the light turns on and the razor charges.

So it looks obvious that there is some sort of bad contact with the two pins on the razor end.

I'd like to read your suggestions about how to fix the bad contact but I'm also a little bit concerned about safety... like not setting my house on fire for a 30$ razor.

Thanks!